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A question about transposition table

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Hi, I have a question about transposition tables. I am trying to compare the effectiveness of an algorithm with and without a TT. A couple of definitions first: D = depth of current node Dm = maximum search depth Dtt = depth of a result for the current node stored in the TT (i. e. depth of a subtree that generated this result) A0 = an algorithm that doesn't use a TT A1 = an algorithm that uses a TT, but returns the result only if Dtt == Dm - D A2 = an algorithm that uses a TT, returns the results if Dtt >= Dm - D Obviously the A1 algorithm plays exactly the same way as A0, only faster. Now A2 is returning more (and deeper) TT results than A1, and so it plays differently. My question is, whether the number of nodes visited by A2 must always be lower than the number of nodes visited by A1 (at least on average). I thought yes, but my results don't confirm that. Does anyone know? Maybe my implementation is wrong, but in my tests the number of nodes visited by A2 (and thus the search time) was almost always greater than that of A1. Certainly A2 should have more accurate results and therefore be more successful, but I am curious about the performance as well.

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